Recently, a new concept called multiplicative differential was introduced by Ellingsen et al. [7]. As an extension of the differential uniformity, it is theoretically appealing to determine the properties of c-differential uniformity and the corresponding c-differential spectrum. In this paper, based on certain quadratic character sums and two special elliptic curves over \(\mathbb {F}_p\) , the \((-1)\) -differential spectra of the following two classes of power functions over \(\mathbb {F}_{p^n}\) is completely determined: (1) \(f_1(x)=x^{\frac{p^n+3}{2}}\) , where \(p>3\) and \(p\equiv 3\pmod 4\) ; (2) \(f_2(x)=x^{p^n-3}\) , where \(p>3\) . The obtained result shows that the \((-1)\) -differential spectra of \(f_1(x)\) and \(f_2(x)\) can be expressed explicitly in terms of n. Moreover, an upper bound of the c-differential uniformity of \(f_2(x)\) is given.
